Modeling Pulsed High-Power Spikes to Drive Piezoelectric Broad- band Transducers Improving SNR in Ultrasonic Imaging & NDE

Ultrasonic imaging & NDE applications can greatly improve their signal-to-noise ratios (SNR) by driving each transducer (composing piezoelectric arrays) with a spike giving pulsed power of k-Watts, repetitively at a PRF = 5000 spikes/s, by using a HV capacitive-discharge generator. However very-high levels, of pulsed intensities (3-10 A) and voltages (300-700 V) must be considered for a rigorous spike modeling. Even though the consumed "average" power will be small, the intensity through each transducer achieves several amperes, so the pulsed powers delivered by each HV generator can attain levels higher than in CW high-power ultrasonic applications: e.g., up to 5 kW / spike. This is concluded here from a transient modeling of the loaded generator. Then, unforeseen phenomena rise: intense brief pulses of driving power & emitted force in transducers, and non-linearities in driver semiconductors, because their characteristic curves only include linear ranges. But fortunately, piezoelectric devices working in this intense regime do not show serious heating problems, because the average power remains being moderate. Intensity, power and voltage driving a broadband transducer from a HV capacitive pulser, are calculated to drastically improve (in ≅ 40 dB) the ultrasonic net dynamic range available, with emitted forces ≅ 250 Newtons pp and E/R received pulses of 76 V pp.


of 20
new very efficient emission equipment employed for HR images forming: in particular, high-peak electrical intensities in all the electronic pulsers associated with an imaging array, and elevated peaks of driving power & emitted force in the involved transducers. As a consequence of this, high-peaks (only temporary) in the involved parameters, and notable short-duration non-linear electrical / piezoelectric pulsed responses could appear, due to the associated pulsed regime in this type of efficient HR imaging & NDE applications.
For instance, pulsed but important parameter variation ranges, would be experienced in efficient HV electronic drivers included in the ultrasonic imaging systems under study. Thus, some semiconductor devices included in these electronic pulsers for NDE can enter in the saturation state under pulsed intensities of up to 5-10 amperes. These so high levels could originate non-linear behaviors very different respect to those observed in the low electrical intensity cases. And the high electrical intensities and voltages (300-700 V), supported by some components, could lead to quite surprising temporal electronic responses, which should be taken into account in the modeling and simulation stages, during the design of new equipment for very-efficient ultrasonic imaging purposes.
Really, these non-ideal and non-linear behaviors have not been expected in a broadband ultrasonic channel using low-power transducers, because the total consumed averaged power is rather small in these types of applications. But the pulsed ultrasonic energy repetitively emitted by the involved transducers, and the instantaneous electrical power IEP (in each pulsed shot) delivered by the electronic HV drivers (during each repetitive very-short emission time-period), can attain higher levels, even, than in typical CW highpower ultrasonic applications: for instance, several kW of instantaneous power delivered toward each emitter transducer can be registered during every individual driving.
For comparative purposes, for instance in power CW ultrasonic applications [8] it is usual to register, for the medium power cases, driving peak values as: 600-700 V in voltage, and 0,6-0,7 A in current; i.e., 400-500 W in power. And in the very-high power ultrasonic equipment, values like [1400-1800 V in voltage, 1-1,2 A in current, and 1,5-2 kW in power] can be attained across the electrical terminals of the working ultrasonic transducers.
As other indicative data necessary for understanding -a) why it results necessary to design special driving schemes based on HV capacitive discharges, and -b) the causes of the required pulsed high-power: it must be noted than the typical values of the input resistive impedances of the considered broadband piezoelectric transducers, when they are inductively tuned around their series resonances, usually range between 50 and 300 Ω, for efficient ultrasonic radiations in more usual media; and the capacitances across transducer terminals can attain several nF. Other HV generators, useful with high-impedance ultrasonic transducers, are not efficient options for driving these demanding load impedances.
As a summary of the aspects above described: some unexpected very-high values in pulsed regime, like maximum electrical levels supported by some electronics drivers and piezoelectric transducers, must be taken into account for a rigorous analysis of the whole emission piezoelectric process. This must be made under the specific data of pulsed power and electrical current needed for the efficient driving required, for instance, in ultrasonic imaging for medical and industrial NDE applications with high-resolution and SNR [7]. Finally, some obtained quantitative results will be discussed, in relation to pulsed high-power waveforms at the output of a tuned capacitive driving case with moderated voltage, applied to an emission ultrasonic application as those here analyzed. These results illustrate pulsed magnitudes being comparable to many cases of CW high-power applications, although the CW regime is not employed in imaging and NDE systems. The resulting force and velocity pulses over the transducer emission face, will be also shown.

II. 1. Electronic systems for high resolution & SNR in ultrasonic imaging and NDE
The efficient electronic equipment specifically designed for ultrasonic beam forming, during the images syntheses, widely employed in applications for -a) industrial non-destructive evaluation NDE for quality control of materials and b) high-resolution (HR) medical diagnosis-has the general block diagram detailed in the Figure 1. In each individual driving pulser, a selective damping block works in cascade with a basic H.V. pulse generation unit. The damping block notably reduces certain oscillations induced in driving pulses, due to the more usual emission matching circuits include an inductive tuning for medical and NDE imaging applications [13]. In all the parallel pulse-echo units of Figure 1, both piezoelectric sections share a unique matching circuit (damping and tuning), due to only one of the two sections is simultaneously working, well as an emitter or well as a receiver.
Logically, the periods with high values in pulsed power are those related to each repetitive HV driving. The excitation pulse amplitude, in voltage, are normally 300-500 Volts, but can attain up to 700 Volts. The pulse repetition frequencies (PRF) for pulse-echo imaging vary normally between 2.000 and 10.000 spikes / sg, depending on final imaging resolution (number of emitted foci and lines). The durations of each high-voltage driving spike, varies between 100 and 500 nanoseconds, in the more habitual inspection cases.
These electrical characteristics assure, in all the channels, an efficient transducers excitation repeated several thousands of times in each second, in order to obtain the elevated number of echo-signals that make possible the very fast processes employed nowadays for electronic focusing and scanning of the finally involved pulsed ultrasonic beams.
Each pulser typically includes a number of non-linear circuits, e.g., semiconductor devices [5,16]. These circuits have to support short pulsed intensities of up to ten amperes, and in consequence they can suffer a high-saturation state, with possible non-linear responses. In fact, the characteristics curves of many electronic devices contemplate only linear responses under moderate intensities values (e.g., < 1 Ampere).
But, fortunately, the piezoelectric devices, working in such a high-power transient regime, do not show serious heating problems (which could be potentially destructive), because the associated mean power dissipation remains in the order of the Watt. However, very-high levels in both, pulsed electrical intensities (2-10 A) and voltages in the HV output stages (300-700 V), could lead to transitory non-linear behaviors, which must be considered in the imposed transient regime, for a precise modeling of the time and frequency response of each pulser stage [11][12].
II. 2. Circuits for high intensity transducers driving using HV capacitive discharges.
The capacitive driving pulsers for efficient ultrasonic emission usually include highvoltage negative ramp generators, firstly proposed through a thyristor in [10] and after that through a Mos-Fet power transistor connected to a selective damping network [5]. In the second case, a very-low series impedance and short fall times are obtained. The ramp generator is connected in cascade with specific circuital networks [5] in order to achieve a good electrical matching with broadband emitter transducers and to finally attain highpower spikes for obtaining very high-intensity in the ultrasonic emission process.   The circuital topologies of the HV ramp generator and of the pulse shaper & selective damping, depicted in Figure 2, are detailed in Figure 3.
The HV waveforms across the transducer ZT use to adopt the shape of a "spike" as it is shown in  It must be noted that this capacitive circuital configuration offers the possibility to generate pulses of HV, up to 500-700 V, and high pulsed power (order of k-Watt) across piezoelectric transducers in resonance conditions, even with very low resistive impedance (tens of ohms) and high capacitance in parallel (some nano-Farads).
It is usual, for ultrasonic imaging, to choose widths of spike between 100 and 500 nano-seconds, depending on the central frequency of the broad frequency band related to the input electrical conductance of each piezoelectric transducer to be driven.
Motional influences in a HV driving spike from the piezoelectric transducer  The Figure 5.a), depicts the waveform for this specific transducer driving, calculated from circuital modeling as those explained in the following section. The non-linear mechanical influences from transducer vibrations in the HV spike also clearly appear, which have a similar shape to the emitting surface force, whose calculated waveform is shown in  Improving reception SNR: The global efficiency of the electronic option, analyzed in this section for HV capacitive driving in emission stages, has a very important influence on the finally received ultrasonic signal values, in emission-reception NDE schemes. As an indicative example, the amplitude of the resulting broadband signals received by throughtransmission thru a 2 cm thickness methacrylate piece located between two broadband transducers, can attain values so high as 50-70 Volts peak-to-peak [9,13], measured directly in receiver transducer terminals, without applying any type of reception amplifier.
In this referenced case, the two similar broadband piezoelectric transducers employed to obtain so intense received signals were the backed (6 Mrayl As values of reference, it must be noted that the usually reported pulsed echo-signals (received in similar ultrasonic applications) move around the range of hundreds of mV.
This extremely advantageous results suppose a high SNR improvement, in the final E/R broadband responses in the received stage (i.e., ultrasonic waveforms) > 37 dB respect to habitual values in similar ultrasonic situations. This is the main consequence of applying a high-efficiency electronic driving system of the tuned capacitive type, as those analyzed in this paper. In this case, an adequate inductive tuning of the employed transducers (56 µH // 100 Ω in emission and 22 µH // 1,5 kΩ in reception) was also an aspect of notable influence in the results, by a duplication of amplitude and bandwidth, simultaneously [9].
A priory, it is not an easy election to decide the more favorable selection of values for the coupling electrical components in the imaging & NDE emission stages: damping resistance RD, inductive tuning in emission L0 and discharge capacitor C. In the following section, some modeling tools are described, very useful in order to assist in the design process of an optimum HV efficient driving system for each selected working transducer.

II. 3. Methods y Schemes for modelling and simulations of tuned HV capacitive drivers
In this section, a description is made firstly of equations in time and spectral domains describing the driving voltage DV from an inductively tuned HV capacitive driver.
By means of these expressions, a linear analysis could be made about the responses of this type of HV driver, using classical methods, but the presence of many non-linear electrical elements, in the circuital topology under study in this work, prevents in many cases the obtaining of driving waveforms as those encountered in the applications with real equipment containing the above described HV capacitive driver ( Figure 3). But, in many emission cases by using this mathematic way, a linear expression could be obtained, but only for the main part of DV (Driving Voltage), just the first negative HV pulse [5,7], and only by considering a simplification applicable uniquely in some cases. So, in some situations encountered in the practice, a possible linear option is to analyze this circuit in the frequency domain, taking into account that the effects produced by RL (a few ohms) and by the network of diodes D1-D2 in Figure 3, can be disregarded in principle, under certain conditions. Then, a time response can be obtained [7] by means of the inverse Laplace transformation of the following analytical expression for DV(s): where: CS = C + CXT, being CXT the transducer static capacitance; and Req is given by: In (3) Nevertheless, now, in this point of the analysis, these effects could be just approximated, by emulating the cancelling (to putting at "cero") of the oscillatory response at the final of the first ascendant zero-crossing, just after the launching of the high-voltage spike, and so preventing an undesired lengthening on the driving pulse [9]. But this option is somewhat inaccurate in respect to the real experimental waveforms for tuned HV driving.
For obtaining a more accurate numerical simulation of this complex HV capacitive driving process, as needed here for an efficient quantization of the waveforms corresponding to the instantaneous electrical intensity and the pulsed power through the transduction stage, a non-analytical option must be employed, based in some circuital models containing the non-linear semiconductors under electrical high-intensities.

Some circuital solutions applicable for non-linear modelling and numerical simulations of tuned capacitive generators of pulsed high-power spikes
A practical solution for non-linear modelling of HV capacitive drivers is to apply software developed by authors, to implement and connect some PSpice circuital simulations of all the electronic/piezoelectric/ultrasonic subsystems involved, which use distinct equivalent circuits specifically created by us for the whole high-voltage emitters [6,12,18].
For instance, a quadratic approach can be implemented for the frequency dependence of mechanical losses in the piezo-electric transducer (XT), and non-ideal electrical effects can be considered [11,16,18]. These and other improvements are show in the following.
A first scheme including some non-ideal behaviors is shown in Figure 6, which are very useful to improve the modeling of HV transducer driving in the high frequency range  Other simpler option applicable for non-linear modelling and simulation of capacitive generators of pulsed high-power spikes is shown in the Figure 7. It is specifically adequate for a lower working frequency ultrasonic range, from 0,5 to 4 MHz.
In this alternative circuital option, the electronic driving section, giving an excitation voltage V, can be modeled by means of an HV ramp generator (VG) from a HV supply (V0), and including the diode networks, SM1 and SM2, and the parallel combination (impedance Zp) of the resistive and inductive tuned damping components (RD and L0 in Fig. 3.b). In this circuital representation case of Figure 7, a PSpice modeling of both emission & reception stages is included, by means of: i) a simple implementation of the HV spike generator connected to the E/R basic piezoelectric emitter sections, and ii) the circuital concretion of the emitted and receiver impedance matching layers to the propagation medium; this is taken into account by means of two transmission lines Tlayer 1-2 in Fig. 7.b.
Here, Rf represents the acoustic impedance of the propagation media, and Rb1 and Rb2 are the acoustic impedances of the E/R transducers backing sections [14][15]18]. Results are shown related to the pulsed electrical output intensity flowing through the transduction stage, and to the pulsed power delivered from a tuned HV capacitive pulser with a circuital scheme as that of Figure 3. These results were obtained by applying a non-analytical modeling, a necessary solution because the involved circuits contain several non-linear behaviors in some semiconductors, which can be described by means of explicit circuital models in moderate frequency range with piezoelectric losses (Figure 7).
This practical solution for the analysis, here employed to study the mentioned non -linear / ideal-responses, introduces a global circuital modelling of the involved electronicpiezoelectric-ultrasonic blocks. In this line, an implementation in the PSpice context was employed, from two coupled equivalent circuits with parameters related to this case.
A software specifically created by us, for the analysis of these pulsed high-power capacitive generators electrically matched to a broadband transducer, was specifically adapted. In this way, the numerical simulation [12,18] of the overall driving-transduction sub-systems, involved in this particular application for transducer driving, was made.
Our practical objective was obtained by simulation and numerical calculation of a set of the more important waveforms produced in the loaded output of the capacitive high power pulser (as that shown in Figure 3), and of the subsequent mechanical pulsed waveforms radiation from the driven transducer to the propagation medium (across Rf in Fig.7).
These output waveforms are quite adequate for estimating the final efficiency associated to a typical broadband channel valid for efficient industrial ultrasonic diagnosis, that uses a piezoelectric transducer with a wideband centered around 1 MHz, and containing both parallel electrical tuning L0 and electrical damping RD. In the following and last paper section, the consequences of the above depicted graphic results are discussed, in relation to the possible obtention, for ultrasonic NDE and imaging applications, of high amplitude received signals with high SNR from the driving spikes with pulsed power of k-Watts. Also, some additional details, around the modeling & simulation methods employed for the calculations, are specifically analyzed. The final advantages of the here analyzed tuned HV capacitive-discharge driving (for transducers with low and medium input impedances) over others circuital topologies for HV pulsers, are also specified and commented, including some generators designed for the excitation of high-impedance transducers non demanding so high electrical currents.
IV. Discussion and Conclusions the common PRF used in imaging cases, was of only a few Watt. This very intense pulsed regime, during all the necessary electrical driving cycles in these types of E/R applications, was performed for an elevated pulse repetition frequency (the typical in imaging), and also for other additional experiments working at a bigger PRF of 10 kHz.
As additional electrical data referred to the pulser output parameters, in the here studied particular HV driving case, the pulsed electrical current flowing through the emission transducer attained 6 amperes pp during each electrical driving with output voltage pulses rather of moderated value, near to 400 Volts.
The application of non-linear modeling [11,18] and associated simulation software [6,12], both developed by the authors, for obtaining the electrical parameters values in the HV driving outputs and the pulsed mechanical waveforms emitted by the transducer (here considered for creating the pulses depicted in Figure 8), has proven that those computer tools are adequate to accurately represent the effects of an intense electrical excitation.
In addition, the subsequent improved emitted waveforms from the transducer face (force and vibration velocity) were also calculated for this efficient driving (including non-ideal effects), being these simulated waveforms coherent with previous typical data.
High The new high-power generators, to be employed for high SNR ultrasonic NDE and HR imaging of inner parts in the inspected pieces, must be carefully designed for an adequate driving of each efficient PZT piezoelectric transducer with brief pulses having power enough to achieve high dynamic ranges in the finally acquired signals in reception. This high power is needed by the low working input resistance (tens or hundreds of ohms) of these tuned broadband transducers in MHz range; this resistance is the electrical consequence (in transducer terminals) of Rmotional in the mechanical branch, when a transducer radiates in its series resonance (i.e., at its frequency of maximum electrical conductance).
To solve this strong requirement in PZT transducers needs of high-power capacitive generators, as those here analyzed, providing short output pulses with maintained high electrical currents (up to 5-10 A), through inductively tuned transducers in working conditions, i.e. mechanically loaded with specific acoustic impedances of several MRayls.
In fact, other HV generators of pulses up to 1000 V, designed to be useful with air coupled transducers [21] or purely capacitive loads [22] Paper results confirm the special adequation, of this type of pulsed high-power capacitive-discharges driving, to the very-efficient broadband applications here considered.
In particular, the achievement of signal-to-noise ratios (SNR) and related dynamic ranges as high as those investigated here (for both ultrasonic emission and reception processes) can be illustrated from the following data and conclusions found along our work: -By using the here analyzed capacitive high-power pulsed excitation (with a rather moderated spike voltage of 400 V), the resulting force emitted for the selected backed transducer (with λ/4 coupling layer to methacrylate materials) attains a value of 250 Newton pp in its radiating face, as it was shown during the first cycle of the emitted short pulse.
-As a consequence of this notable force level promoted by the capacitive driving option, it is possible to easily radiate acoustic fields (over all the aperture projection), with average values in the order of the MPascal pp, by using simple unfocused transducers.
-The driving of the broadband transducer employed in this paper, with the here designed high-power spikes, made it possible to obtain received ultrasonic waveforms (in a E/R application) having short-time duration and with very-high amplitudes: e.g. 76 Vpp directly at receiver transducer terminals, in a through-transmission (TT) regime through a methacrylate plate. This supposes improvements in SNR of up to 38 dB (without using any type of amplification, averaging or filtering), respect to the received signals in classical ultrasonic TT and pulse-echo imaging & NDE applications inside of solid or liquids media.
And this SNR improvement could be extended 4,9 dB more by using spikes of 700 V, when this voltage can be electrically supported by the driven broadband transducer.
-Thus, from all the quite efficient results above shown, it is possible to predict that the circuital topology, analyzed in this paper, can originate pulsed high-power driving spikes, with low output impedances (1-2 Ω), very adequate for an efficient excitation of broadband piezoelectric transducers, being able to improve the final obtained SNR in broadband applications. This implies a possible extension of the net dynamic ranges available in current ultrasonic imaging & NDE (≅ ranging between 30 and 70 dB) up to > 70 and 110 dB.
This drastic improvement could be decisive, particularly for cases with high attenuations or low acoustic impedances in some inspected media: lung, wood, foam, cork, benzene, gases, etc., where e.g. losses of up to 74 dB are registered along only the 2 short internal paths between emitting and receiving faces of the matched PZT ceramics and the medium.
In addition, internal piezoelectric losses and medium attenuation should be added.
As a final general conclusion, this paper has shown for high-power capacitive spike generators driving broadband transducers, that though the finally consumed "averaged" power (for all the necessary thousands of spikes during a second, in ultrasonic imaging) can be very small (a few watts), the repetitive pulsed intensities through the transducer can attain several amperes during each spike with rather moderate peak voltages (400 V).
In consequence, the delivered pulsed power from this type of HV generators can arrive to levels typical in CW high-power ultrasounds: in particular, driving spikes with pulsed